Putting the tank in the closet is a little easier as long as you have proper ventilation. (Not shutting it up in the closet with the doors closed) As an adult blood, to set it up in the closet would require quite a bit of fabrication as I'm sure you know. But for everyone else, it's not that bad an idea if he has a way to keep the heat and humidity right. It would be just like using an entire room for an enclosure (which I know has worked for many) except smaller. Mike the only issue I can think of is ventilation. So depending on what your idea is for the door to the closet, you'll have to factor that in. Dead air, warm temps, and high humidity can also grow great mold. And if you're going to do this, it seems that you should also at least build some sort of platform at about waist level to be his bottom "floor". That would be easier for maintenance and less chance of you getting nailed in the face kneeling down to change his water.
Other than that, it sounds like a fun project and definitely a feasible one to me. Good luck.